Estimation of the incidence for non-terminal events in presence of a terminal event and evaluation of covariate effects: Sub-distribution and marginal distributions based on copulas. An application to disease progression on a breast cancer trial dataset

In clinical studies, during follow-up several kinds of events related to disease progression may be observed. In the semi-competing risks setting, some events, such as death, may prevent the observation of disease progression, thus acting as competitor for the event of interest. Methods of analysis specific for semi-competing risks data referring to marginal distribution of the non-competing events constitute a recent area of methodological research which has received a great impulse in latest years. However in clinical applications the analysis is traditionally based on crude cumulative incidences, and inference on marginal distributions is seldom considered, even when the principal aim concerns the probability of observing disease progression and death occurred without progression is a \u201cnuisance\u201d. Aim of this work is making a comparative review of semi-parametric marginal and sub-distribution methods of analysis, with particular reference to marginal regression models based on copulas. More specifically, two structures were considered for marginal models: in the first one all parameters are time-dependent, while in the second one parameters vary with covariates but does not depend on time. Applications to breast cancer clinical trial data and to a simulated dataset are reported, to show the differences and the similarities among marginal and sub-distribution approaches. Results highlight that, when the competing event acts during the whole follow-up, the marginal approach became essential for the correct estimation of marginal incidences and covariate effects. Regression methods based on copulas are promising, however there is a need of refinements concerning model building strategies, and, of standardised software routine for the practical application of these methods

Contribution of 3H-thymidine labelling index and flow cytometric S-phase in predicting survival of patients with non-Hodgkin's lymphoma.

The 3H-thymidine labelling index (3H-dT LI) of cell suspensions from fresh material and the flow cytometric S-phase (FCM-S) of nuclei recovered from paraffin blocks were determined on the same pathologic lymph node specimen for 190 non-Hodgkin's lymphomas (NHLs). FCM-S was defined by a planimetric method and by an optimization procedure. Poor correlation coefficients were observed among the three cell kinetic variables. All three cell kinetic variables were significant indicators of 8-year survival and median survival time. The life-regression procedure evidenced a significant relative contribution of 3H-dT LI and FCM-S, thus suggesting a different biologic meaning of the two cell kinetic variables. This finding was further supported by evidence that simultaneous use of 3H-dT LI and FCM-S can identify groups of patients with different survival better than when either modality is used alone. Multivariate analysis indicated that the risk groups as defined by cell kinetic variables are predictors of survival even in the presence of established factors such as histology and stage

Value of epidermal growth factor receptor status compared with growth fraction and other factors for prognosis in early breast cancer.

The epidermal growth factor receptor (EGFR) is a transmembrane glycoprotein whose expression is important in the regulation of breast cancer cell growth. The relationship between EGFR status (determined by an immunocytochemical assay) and various prognostic factors was investigated in 164 primary breast cancers. Overall 56% of tumours were EGFR-positive and the expression of EGFR was unrelated to axillary node status, tumour size and histological grade; and it was poorly associated with the tumour proliferative activity measured by Ki-67 immuno-cytochemistry. The relapse-free survival (RFS) probability at 3-years was significantly worse for patients with EGFR positive tumours (P = 0.003) and for those whose Ki-67 score was > 7.5% (P = 0.0027), as well as in patients with axillary node involvement (P = 0.01) and with poorly differentiated tumours (P = 0.04). Immunocytochemical determination of EGFR and cell kinetics gave superimposable prognostic information for predicting RFS with odds ratios of 3.51, when evaluated singly. In our series of patients EGFR, Ki-67 and node status retain their prognostic value concerning RFS in multivariate analysis. The 3-year probability of overall survival (OS) was significantly better in node-negative patients (P = 0.04) and was similar in EGFR-positive and negative patients. In conclusion, EGFR status appears to be a significant and independent indicator of recurrence in human breast cancer and the concomitant measurement of the tumour proliferative activity seems to improve the selection of patients with different risks of recurrence

Estimation of the Piecewise Exponential Model by Bayesian P-Splines via Gibbs Sampling: Robustness and Reliability of Posterior Estimates

In the investigation of disease dynamics, the effect of covariates on the hazard function is a major topic. Some recent smoothed estimation methods have been proposed, both frequentist and Bayesian, based on the relationship between penalized splines and mixed models theory. These approaches are also motivated by the possibility of using automatic procedures for determining the optimal amount of smoothing. However, estimation algorithms involve an analytically intractable hazard function, and thus require ad-hoc software routines. We propose a more user-friendly alternative, consisting in regularized estimation of piecewise exponential models by Bayesian P-splines. A further facilitation is that widespread Bayesian software, such as WinBUGS, can be used. The aim is assessing the robustness of this approach with respect to different prior functions and penalties. A large dataset from breast cancer patients, where results from validated clinical studies are available, is used as a benchmark to evaluate the reliability of the estimates. A second dataset from a small case series of sarcoma patients is used for evaluating the performances of the PE model as a tool for exploratory analysis. Concerning breast cancer data, the estimates are robust with respect to priors and penalties, and consistent with clinical knowledge. Concerning soft tissue sarcoma data, the estimates of the hazard function are sensitive with respect to the prior for the smoothing parameter, whereas the estimates of regression coefficients are robust. In conclusion, Gibbs sampling results an efficient computational strategy. The issue of the sensitivity with respect to the priors concerns only the estimates of the hazard function, and seems more likely to occur when non-large case series are investigated, calling for tailored solutions

Estimating Relapse Free Survival as a Net Probability : Regression Models and Graphical Representation : An Application of a Large Breast Cancer Case Series

In most clinical studies, the evaluation of the effect of a therapy and the impact of prognostic factors is based on relapse-free survival. Relapse free is a net survival, since it is interpreted as the relapsefree probability that would be observed if all patients experienced relapse sooner or later. Death without evidence of relapse prevents the subsequent observation of relapse, acting in a semi-competing risks framework. Relapse free survival is often estimated by standard regression models after censoring times to death. The association between relapse and death is thus accounted for. However, to better estimate relapse free survival, a bivariate distribution of times to events needs to be considered, for example by means of copula models. We concentrate here on the copula graphic estimator, for which a pertinent regression model has been developed. No direct parametric estimation of the regression coefficient for the covariates is available and the evaluation of the impact of covariates on relapse free survival is based on graphical representation for each covariate singularly. The advantage of this approach is based on the relationship between net survival, and crude cumulative incidences. Regression models can be fitted for the latter quantities and the estimates can be used to compute net survival through a copula structure. Our proposal is based on flexible regression transformation model on crude cumulative incidences based on pseudo-values. An overall view of the joint association among covariates and relapse free survival is obtained through Multiple Correspondence Analysis. Moreover cluster analysis on MCA coordinates was used to synthesize covariate patterns and to estimates the corresponding relapse free survival curve. This approach has been applied to a large \u201chistorical\u201d case series of patients with breast cancer

Long-term follow-up of elderly patients with operable breast cancer treated with surgery without axillary dissection plus adjuvant tamoxifen.

Between 1982 and 1990, 321 elderly patients (range 70-92 years, median age 77) with operable breast cancer (T1 in 219, T2 in 77, T3 in one and T4b in 24 patients) and clinically uninvolved axillary nodes underwent surgery without axillary dissection and received adjuvant tamoxifen. All patients had surgery performed under local anaesthesia. Tamoxifen was given after surgery at the dose of 20 mg daily, indefinitely. With a median follow-up of 67 months (range 42-141), 17 patients developed local relapse, 14 ipsilateral axillary recurrence, five ipsilateral breast cancer, five contralateral breast cancer, 13 second primary and 23 developed distant metastases. The cumulative probability of developing a local, axillary and distant recurrence at 72 months was estimated to be 5.4%, 4.3% and 6.2%, respectively. Out of 244 patients who did not develop any relapse, 83 (25.8%) died from intercurrent disease. The 72 month relapse-free survival rate was 76%. This experience suggests that elderly patients with small tumours without clinical axillary involvement may be satisfactorily treated with conservative surgery and tamoxifen. The importance of axillary dissection is controversial owing to a high response rate to hormonal therapy and an increased death rate due to concomitant diseases

Contribution of vascular endothelial growth factor to the Nottingham prognostic index in node-negative breast cancer

The prognostic contribution of intratumour VEGF, the most important factor in tumour-induced angiogenesis, to NPI was evaluated by using flexible modelling in a series of 226 N-primary breast cancer patients in which steroid receptors and cell proliferation were also accounted for. VEGF provided an additional prognostic contribution to NPI mainly within ER-poor tumours. © 2001 Cancer Research Campaignhttp://www.bjcancer.co

Treatment Effects and Risk Factors Evaluation in Longitudinal Studies : A Statistical Help for Data Analysis

This paper was inspired by the experience of the Authors research group composed by oncologist veterinarians and a biostatistician to evaluate treatments and prognostic factors with the aim to help veterinarians involved in longitudinal studies into evaluating and writing prognostic results. Longitudinal studies are commonly analysed by techniques for survival data, taking into account for the time elapsed from the beginning of observation and the occurrence of an event related to treatment effect or disease course. The presence of incomplete follow-up information for some subjects requires specific descriptive and inferential statistical methods. Two literature datasets were analysed to show statistical models implementation techniques and to discuss statistical issues: I) A multicentre clinical trial on remission maintenance of children with acute Lymphoblastic leukaemia and II) A randomized clinical trial on advanced inoperable lung cancer. Data sets concerned studies on \u201chumans\u201d, nevertheless the peculiar data structure allowed to discuss some aspects which are common to survival analysis studies, regardless on subject\u2019s characteristics. Log-rank test was used to compare survival curves for treatments and the relationship between Log-Rank test and univariate Cox model results was explained. As the evaluation of prognostic impact cannot be based only on p-values, the strength of the association between treatments and prognosis was estimated to take into account for the clinical relevance of results. On the second data set, beside of treatment, other clinical variables were available and a multivariate Cox model was applied. Model implementation was discussed concerning the coding of categorical variables and the relationship between continuous variables and model response. Suggested rules for the maximum number of covariates to be included in order to obtain reliable results were cited. Finally, the predictive ability of the model was discussed based on a measure of the area under ROC curve specific for survival data

Investigation on Dabigatran Etexilate and Worsening of Renal Function in Patients with Atrial fibrillation : the IDEA Study

BACKGROUND AND OBJECTIVES: Warfarin-related nephropathy is an unexplained acute kidney injury, and may occur in patients with supratherapeutic INR, in the absence of overt bleeding. Similar findings have been observed in rats treated with dabigatran etexilate. We conducted a prospective study in dabigatran etexilate-treated patients to assess the incidence of dabigatran-related nephropathy and to investigate the possible correlation between dabigatran plasma concentration (DPC) and worsening renal function. METHOD: One hundred and seven patients treated long term with dabigatran etexilate for non-valvular atrial fibrillation (NVAF) were followed up for 90 days. DPC, serum creatinine (SCr) and serum cystatin C were prospectively measured. Ninety five patients had complete follow-up data and were evaluable for primary endpoint. RESULTS: Eleven patients had supratherapeutic DPC, defined as DPC higher than 200 ng/ml at study enrolment, but at the end of follow-up no patient showed a persistent increase in SCr. No patients experienced acute kidney injury. CONCLUSIONS: Our study shows that no persistent renal detrimental effect is associated with dabigatran treatment. An increase in SCr during dabigatran treatment is reversible and it seems to be unrelated to dabigatran itself

Tissue carcinoembryonic antigen and oestrogen receptor status in breast carcinoma: an immunohistochemical study of clinical outcome in a series of 252 patients with long-term follow-up.

Carcinoembryonic antigen (CEA) is a well-known tumour marker whose immunohistochemical expression could be prognostically relevant in breast carcinomas. We evaluated CEA immunohistochemical expression, using the specific T84.66 monoclonal antibody, in a series of 252 consecutive cases of infiltrating breast carcinomas (104 N0, 148 N1/2) with median follow-up of 84 months. Oestrogen receptor (ER) status has been evaluated with the immunohistochemical method (ER1D5 antibody, 10% cut-off value): 121 cases were ER negative, 128 cases were ER positive and in three cases ER status was unknown. CEA staining was cytoplasmic; staining intensity and percentage of reacting cells were combined to obtain a final score (CEA score). The difference between the distribution of CEA score within the modalities of the other variables was not statistically significant. Univariate survival analysis has been performed on the series of node-negative and node-positive patients. In the latter subgroup, this has been performed separately for patients treated with systemic adjuvant hormonal therapy or chemotherapy. A multivariate analysis was only performed for node-positive patients treated with adjuvant therapy. CEA immunoreactivity was not prognostically relevant in any subset of analysed patients. The most important prognostic markers were nodal status and tumour size